Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,6,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.85880717084\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 13x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 30.2 | ||
Root | \(3.12250 + 1.80278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.30 |
Dual form | 49.6.c.g.18.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.176777 | − | 0.306186i | −0.763998 | − | 0.645219i | \(-0.776766\pi\) |
0.940775 | + | 0.339032i | \(0.110100\pi\) | |||||||
\(3\) | 12.4900 | + | 21.6333i | 0.801234 | + | 1.38778i | 0.918805 | + | 0.394713i | \(0.129156\pi\) |
−0.117571 | + | 0.993064i | \(0.537511\pi\) | |||||||
\(4\) | 14.0000 | + | 24.2487i | 0.437500 | + | 0.757772i | ||||
\(5\) | 37.4700 | − | 64.8999i | 0.670284 | − | 1.16097i | −0.307540 | − | 0.951535i | \(-0.599506\pi\) |
0.977824 | − | 0.209430i | \(-0.0671608\pi\) | |||||||
\(6\) | 49.9600 | 0.566558 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 120.000 | 0.662913 | ||||||||
\(9\) | −190.500 | + | 329.956i | −0.783951 | + | 1.35784i | ||||
\(10\) | −74.9400 | − | 129.800i | −0.236981 | − | 0.410463i | ||||
\(11\) | 142.000 | + | 245.951i | 0.353840 | + | 0.612868i | 0.986919 | − | 0.161219i | \(-0.0515425\pi\) |
−0.633079 | + | 0.774087i | \(0.718209\pi\) | |||||||
\(12\) | −349.720 | + | 605.733i | −0.701079 | + | 1.21431i | ||||
\(13\) | −524.580 | −0.860901 | −0.430450 | − | 0.902614i | \(-0.641645\pi\) | ||||
−0.430450 | + | 0.902614i | \(0.641645\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1872.00 | 2.14821 | ||||||||
\(16\) | −328.000 | + | 568.113i | −0.320312 | + | 0.554798i | ||||
\(17\) | −74.9400 | − | 129.800i | −0.0628914 | − | 0.108931i | 0.832865 | − | 0.553476i | \(-0.186699\pi\) |
−0.895757 | + | 0.444545i | \(0.853366\pi\) | |||||||
\(18\) | 381.000 | + | 659.911i | 0.277168 | + | 0.480070i | ||||
\(19\) | 1086.63 | − | 1882.10i | 0.690554 | − | 1.19607i | −0.281103 | − | 0.959678i | \(-0.590700\pi\) |
0.971657 | − | 0.236397i | \(-0.0759665\pi\) | |||||||
\(20\) | 2098.32 | 1.17300 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 568.000 | 0.250202 | ||||||||
\(23\) | −748.000 | + | 1295.57i | −0.294837 | + | 0.510673i | −0.974947 | − | 0.222437i | \(-0.928599\pi\) |
0.680110 | + | 0.733110i | \(0.261932\pi\) | |||||||
\(24\) | 1498.80 | + | 2596.00i | 0.531148 | + | 0.919975i | ||||
\(25\) | −1245.50 | − | 2157.27i | −0.398560 | − | 0.690326i | ||||
\(26\) | −524.580 | + | 908.599i | −0.152187 | + | 0.263596i | ||||
\(27\) | −3447.24 | −0.910043 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4366.00 | −0.964026 | −0.482013 | − | 0.876164i | \(-0.660094\pi\) | ||||
−0.482013 | + | 0.876164i | \(0.660094\pi\) | |||||||
\(30\) | 1872.00 | − | 3242.40i | 0.379754 | − | 0.657754i | ||||
\(31\) | −3222.42 | − | 5581.39i | −0.602251 | − | 1.04313i | −0.992479 | − | 0.122412i | \(-0.960937\pi\) |
0.390228 | − | 0.920718i | \(-0.372396\pi\) | |||||||
\(32\) | 2576.00 | + | 4461.76i | 0.444704 | + | 0.770250i | ||||
\(33\) | −3547.16 | + | 6143.86i | −0.567017 | + | 0.982102i | ||||
\(34\) | −299.760 | −0.0444709 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10668.0 | −1.37191 | ||||||||
\(37\) | 6315.00 | − | 10937.9i | 0.758349 | − | 1.31350i | −0.185343 | − | 0.982674i | \(-0.559340\pi\) |
0.943692 | − | 0.330825i | \(-0.107327\pi\) | |||||||
\(38\) | −2173.26 | − | 3764.20i | −0.244148 | − | 0.422876i | ||||
\(39\) | −6552.00 | − | 11348.4i | −0.689783 | − | 1.19474i | ||||
\(40\) | 4496.40 | − | 7787.99i | 0.444339 | − | 0.769618i | ||||
\(41\) | 9442.44 | 0.877252 | 0.438626 | − | 0.898670i | \(-0.355465\pi\) | ||||
0.438626 | + | 0.898670i | \(0.355465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1356.00 | −0.111838 | −0.0559189 | − | 0.998435i | \(-0.517809\pi\) | ||||
−0.0559189 | + | 0.998435i | \(0.517809\pi\) | |||||||
\(44\) | −3976.00 | + | 6886.63i | −0.309610 | + | 0.536260i | ||||
\(45\) | 14276.1 | + | 24726.9i | 1.05094 | + | 1.82028i | ||||
\(46\) | 1496.00 | + | 2591.15i | 0.104241 | + | 0.180550i | ||||
\(47\) | 5020.98 | − | 8696.59i | 0.331546 | − | 0.574254i | −0.651269 | − | 0.758847i | \(-0.725763\pi\) |
0.982815 | + | 0.184592i | \(0.0590965\pi\) | |||||||
\(48\) | −16386.9 | −1.02658 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4982.00 | −0.281824 | ||||||||
\(51\) | 1872.00 | − | 3242.40i | 0.100781 | − | 0.174559i | ||||
\(52\) | −7344.12 | − | 12720.4i | −0.376644 | − | 0.652367i | ||||
\(53\) | −7075.00 | − | 12254.3i | −0.345969 | − | 0.599235i | 0.639561 | − | 0.768741i | \(-0.279116\pi\) |
−0.985529 | + | 0.169505i | \(0.945783\pi\) | |||||||
\(54\) | −3447.24 | + | 5970.79i | −0.160874 | + | 0.278643i | ||||
\(55\) | 21283.0 | 0.948692 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 54288.0 | 2.21318 | ||||||||
\(58\) | −4366.00 | + | 7562.13i | −0.170417 | + | 0.295171i | ||||
\(59\) | −18697.5 | − | 32385.1i | −0.699285 | − | 1.21120i | −0.968715 | − | 0.248177i | \(-0.920169\pi\) |
0.269430 | − | 0.963020i | \(-0.413165\pi\) | |||||||
\(60\) | 26208.0 | + | 45393.6i | 0.939844 | + | 1.62786i | ||||
\(61\) | −17798.2 | + | 30827.5i | −0.612425 | + | 1.06075i | 0.378406 | + | 0.925640i | \(0.376472\pi\) |
−0.990831 | + | 0.135111i | \(0.956861\pi\) | |||||||
\(62\) | −12889.7 | −0.425856 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10688.0 | −0.326172 | ||||||||
\(65\) | −19656.0 | + | 34045.2i | −0.577048 | + | 0.999476i | ||||
\(66\) | 7094.32 | + | 12287.7i | 0.200471 | + | 0.347225i | ||||
\(67\) | 1822.00 | + | 3155.80i | 0.0495863 | + | 0.0858859i | 0.889753 | − | 0.456442i | \(-0.150876\pi\) |
−0.840167 | + | 0.542328i | \(0.817543\pi\) | |||||||
\(68\) | 2098.32 | − | 3634.40i | 0.0550300 | − | 0.0953147i | ||||
\(69\) | −37370.1 | −0.944933 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 35632.0 | 0.838869 | 0.419435 | − | 0.907786i | \(-0.362228\pi\) | ||||
0.419435 | + | 0.907786i | \(0.362228\pi\) | |||||||
\(72\) | −22860.0 | + | 39594.7i | −0.519691 | + | 0.900131i | ||||
\(73\) | 20383.7 | + | 35305.6i | 0.447688 | + | 0.775418i | 0.998235 | − | 0.0593859i | \(-0.0189143\pi\) |
−0.550547 | + | 0.834804i | \(0.685581\pi\) | |||||||
\(74\) | −12630.0 | − | 21875.8i | −0.268117 | − | 0.464392i | ||||
\(75\) | 31112.6 | − | 53888.6i | 0.638679 | − | 1.10623i | ||||
\(76\) | 60851.3 | 1.20847 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −26208.0 | −0.487750 | ||||||||
\(79\) | 27308.0 | − | 47298.8i | 0.492291 | − | 0.852674i | −0.507669 | − | 0.861552i | \(-0.669493\pi\) |
0.999961 | + | 0.00887848i | \(0.00282614\pi\) | |||||||
\(80\) | 24580.3 | + | 42574.3i | 0.429400 | + | 0.743743i | ||||
\(81\) | 3235.50 | + | 5604.05i | 0.0547935 | + | 0.0949051i | ||||
\(82\) | 9442.44 | − | 16354.8i | 0.155078 | − | 0.268603i | ||||
\(83\) | 524.580 | 0.00835827 | 0.00417913 | − | 0.999991i | \(-0.498670\pi\) | ||||
0.00417913 | + | 0.999991i | \(0.498670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11232.0 | −0.168620 | ||||||||
\(86\) | −1356.00 | + | 2348.66i | −0.0197703 | + | 0.0342432i | ||||
\(87\) | −54531.3 | − | 94451.0i | −0.772410 | − | 1.33785i | ||||
\(88\) | 17040.0 | + | 29514.1i | 0.234565 | + | 0.406278i | ||||
\(89\) | −10191.8 | + | 17652.8i | −0.136388 | + | 0.236232i | −0.926127 | − | 0.377212i | \(-0.876883\pi\) |
0.789739 | + | 0.613444i | \(0.210216\pi\) | |||||||
\(90\) | 57104.3 | 0.743126 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −41888.0 | −0.515965 | ||||||||
\(93\) | 80496.0 | − | 139423.i | 0.965088 | − | 1.67158i | ||||
\(94\) | −10042.0 | − | 17393.2i | −0.117219 | − | 0.203030i | ||||
\(95\) | −81432.0 | − | 141044.i | −0.925734 | − | 1.60342i | ||||
\(96\) | −64348.5 | + | 111455.i | −0.712623 | + | 1.23430i | ||||
\(97\) | −183603. | −1.98130 | −0.990650 | − | 0.136427i | \(-0.956438\pi\) | ||||
−0.990650 | + | 0.136427i | \(0.956438\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −108204. | −1.10957 | ||||||||
\(100\) | 34874.0 | − | 60403.5i | 0.348740 | − | 0.604035i | ||||
\(101\) | 37957.1 | + | 65743.6i | 0.370245 | + | 0.641284i | 0.989603 | − | 0.143825i | \(-0.0459403\pi\) |
−0.619358 | + | 0.785109i | \(0.712607\pi\) | |||||||
\(102\) | −3744.00 | − | 6484.80i | −0.0356316 | − | 0.0617158i | ||||
\(103\) | −5470.62 | + | 9475.39i | −0.0508093 | + | 0.0880043i | −0.890311 | − | 0.455352i | \(-0.849513\pi\) |
0.839502 | + | 0.543356i | \(0.182847\pi\) | |||||||
\(104\) | −62949.6 | −0.570702 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28300.0 | −0.244637 | ||||||||
\(107\) | −109094. | + | 188956.i | −0.921173 | + | 1.59552i | −0.123571 | + | 0.992336i | \(0.539435\pi\) |
−0.797602 | + | 0.603184i | \(0.793899\pi\) | |||||||
\(108\) | −48261.3 | − | 83591.1i | −0.398144 | − | 0.689605i | ||||
\(109\) | 48015.0 | + | 83164.4i | 0.387089 | + | 0.670458i | 0.992057 | − | 0.125792i | \(-0.0401473\pi\) |
−0.604968 | + | 0.796250i | \(0.706814\pi\) | |||||||
\(110\) | 21283.0 | − | 36863.2i | 0.167707 | − | 0.290476i | ||||
\(111\) | 315497. | 2.43046 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −137422. | −1.01242 | −0.506209 | − | 0.862411i | \(-0.668954\pi\) | ||||
−0.506209 | + | 0.862411i | \(0.668954\pi\) | |||||||
\(114\) | 54288.0 | − | 94029.6i | 0.391239 | − | 0.677645i | ||||
\(115\) | 56055.1 | + | 97090.3i | 0.395249 | + | 0.684591i | ||||
\(116\) | −61124.0 | − | 105870.i | −0.421761 | − | 0.730512i | ||||
\(117\) | 99932.5 | − | 173088.i | 0.674904 | − | 1.16897i | ||||
\(118\) | −74790.1 | −0.494469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 224640. | 1.42408 | ||||||||
\(121\) | 40197.5 | − | 69624.1i | 0.249595 | − | 0.432311i | ||||
\(122\) | 35596.5 | + | 61654.9i | 0.216525 | + | 0.375032i | ||||
\(123\) | 117936. | + | 204271.i | 0.702884 | + | 1.21743i | ||||
\(124\) | 90227.7 | − | 156279.i | 0.526970 | − | 0.912739i | ||||
\(125\) | 47511.9 | 0.271974 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 170368. | 0.937300 | 0.468650 | − | 0.883384i | \(-0.344741\pi\) | ||||
0.468650 | + | 0.883384i | \(0.344741\pi\) | |||||||
\(128\) | −93120.0 | + | 161289.i | −0.502363 | + | 0.870119i | ||||
\(129\) | −16936.4 | − | 29334.8i | −0.0896082 | − | 0.155206i | ||||
\(130\) | 39312.0 | + | 68090.4i | 0.204017 | + | 0.353368i | ||||
\(131\) | −174123. | + | 301590.i | −0.886498 | + | 1.53546i | −0.0425120 | + | 0.999096i | \(0.513536\pi\) |
−0.843986 | + | 0.536364i | \(0.819797\pi\) | |||||||
\(132\) | −198641. | −0.992279 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7288.00 | 0.0350628 | ||||||||
\(135\) | −129168. | + | 223726.i | −0.609987 | + | 1.05653i | ||||
\(136\) | −8992.80 | − | 15576.0i | −0.0416915 | − | 0.0722118i | ||||
\(137\) | 37781.0 | + | 65438.6i | 0.171978 | + | 0.297874i | 0.939111 | − | 0.343613i | \(-0.111651\pi\) |
−0.767134 | + | 0.641487i | \(0.778318\pi\) | |||||||
\(138\) | −37370.1 | + | 64726.9i | −0.167042 | + | 0.289326i | ||||
\(139\) | −97047.3 | −0.426036 | −0.213018 | − | 0.977048i | \(-0.568329\pi\) | ||||
−0.213018 | + | 0.977048i | \(0.568329\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 250848. | 1.06258 | ||||||||
\(142\) | 35632.0 | − | 61716.4i | 0.148293 | − | 0.256850i | ||||
\(143\) | −74490.3 | − | 129021.i | −0.304621 | − | 0.527619i | ||||
\(144\) | −124968. | − | 216451.i | −0.502218 | − | 0.869868i | ||||
\(145\) | −163594. | + | 283353.i | −0.646171 | + | 1.11920i | ||||
\(146\) | 81534.7 | 0.316563 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 353640. | 1.32711 | ||||||||
\(149\) | −180515. | + | 312661.i | −0.666113 | + | 1.15374i | 0.312870 | + | 0.949796i | \(0.398710\pi\) |
−0.978982 | + | 0.203945i | \(0.934624\pi\) | |||||||
\(150\) | −62225.2 | − | 107777.i | −0.225807 | − | 0.391110i | ||||
\(151\) | −16140.0 | − | 27955.3i | −0.0576051 | − | 0.0997750i | 0.835785 | − | 0.549057i | \(-0.185013\pi\) |
−0.893390 | + | 0.449282i | \(0.851680\pi\) | |||||||
\(152\) | 130396. | − | 225852.i | 0.457777 | − | 0.792893i | ||||
\(153\) | 57104.3 | 0.197215 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −482976. | −1.61472 | ||||||||
\(156\) | 183456. | − | 317755.i | 0.603560 | − | 1.04540i | ||||
\(157\) | −66434.3 | − | 115068.i | −0.215101 | − | 0.372566i | 0.738203 | − | 0.674579i | \(-0.235675\pi\) |
−0.953304 | + | 0.302013i | \(0.902342\pi\) | |||||||
\(158\) | −54616.0 | − | 94597.7i | −0.174051 | − | 0.301466i | ||||
\(159\) | 176733. | − | 306111.i | 0.554403 | − | 0.960255i | ||||
\(160\) | 386091. | 1.19231 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12942.0 | 0.0387448 | ||||||||
\(163\) | 30682.0 | − | 53142.8i | 0.0904513 | − | 0.156666i | −0.817250 | − | 0.576284i | \(-0.804502\pi\) |
0.907701 | + | 0.419617i | \(0.137836\pi\) | |||||||
\(164\) | 132194. | + | 228967.i | 0.383798 | + | 0.664757i | ||||
\(165\) | 265824. | + | 460421.i | 0.760124 | + | 1.31657i | ||||
\(166\) | 524.580 | − | 908.599i | 0.00147755 | − | 0.00255919i | ||||
\(167\) | −380845. | −1.05671 | −0.528356 | − | 0.849023i | \(-0.677192\pi\) | ||||
−0.528356 | + | 0.849023i | \(0.677192\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −96109.0 | −0.258849 | ||||||||
\(170\) | −11232.0 | + | 19454.4i | −0.0298081 | + | 0.0516292i | ||||
\(171\) | 414006. | + | 717079.i | 1.08272 | + | 1.87533i | ||||
\(172\) | −18984.0 | − | 32881.3i | −0.0489290 | − | 0.0847476i | ||||
\(173\) | 258655. | − | 448004.i | 0.657062 | − | 1.13806i | −0.324311 | − | 0.945951i | \(-0.605132\pi\) |
0.981373 | − | 0.192114i | \(-0.0615343\pi\) | |||||||
\(174\) | −218125. | −0.546176 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −186304. | −0.453357 | ||||||||
\(177\) | 467064. | − | 808979.i | 1.12058 | − | 1.94090i | ||||
\(178\) | 20383.7 | + | 35305.6i | 0.0482206 | + | 0.0835205i | ||||
\(179\) | −305282. | − | 528764.i | −0.712145 | − | 1.23347i | −0.964050 | − | 0.265720i | \(-0.914390\pi\) |
0.251905 | − | 0.967752i | \(-0.418943\pi\) | |||||||
\(180\) | −399730. | + | 692352.i | −0.919571 | + | 1.59274i | ||||
\(181\) | 433828. | 0.984285 | 0.492142 | − | 0.870515i | \(-0.336214\pi\) | ||||
0.492142 | + | 0.870515i | \(0.336214\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −889200. | −1.96278 | ||||||||
\(184\) | −89760.0 | + | 155469.i | −0.195451 | + | 0.338531i | ||||
\(185\) | −473246. | − | 819686.i | −1.01662 | − | 1.76083i | ||||
\(186\) | −160992. | − | 278846.i | −0.341210 | − | 0.590993i | ||||
\(187\) | 21283.0 | − | 36863.2i | 0.0445070 | − | 0.0770883i | ||||
\(188\) | 281175. | 0.580205 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −325728. | −0.654593 | ||||||||
\(191\) | −170596. | + | 295481.i | −0.338365 | + | 0.586065i | −0.984125 | − | 0.177475i | \(-0.943207\pi\) |
0.645760 | + | 0.763540i | \(0.276541\pi\) | |||||||
\(192\) | −133493. | − | 231217.i | −0.261340 | − | 0.452654i | ||||
\(193\) | 308079. | + | 533608.i | 0.595345 | + | 1.03117i | 0.993498 | + | 0.113849i | \(0.0363180\pi\) |
−0.398153 | + | 0.917319i | \(0.630349\pi\) | |||||||
\(194\) | −183603. | + | 318010.i | −0.350248 | + | 0.606647i | ||||
\(195\) | −982013. | −1.84940 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 231478. | 0.424956 | 0.212478 | − | 0.977166i | \(-0.431847\pi\) | ||||
0.212478 | + | 0.977166i | \(0.431847\pi\) | |||||||
\(198\) | −108204. | + | 187415.i | −0.196146 | + | 0.339736i | ||||
\(199\) | −202563. | − | 350849.i | −0.362599 | − | 0.628040i | 0.625789 | − | 0.779993i | \(-0.284777\pi\) |
−0.988388 | + | 0.151952i | \(0.951444\pi\) | |||||||
\(200\) | −149460. | − | 258872.i | −0.264210 | − | 0.457626i | ||||
\(201\) | −45513.5 | + | 78831.8i | −0.0794604 | + | 0.137629i | ||||
\(202\) | 151828. | 0.261803 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 104832. | 0.176367 | ||||||||
\(205\) | 353808. | − | 612813.i | 0.588008 | − | 1.01846i | ||||
\(206\) | 10941.2 | + | 18950.8i | 0.0179638 | + | 0.0311142i | ||||
\(207\) | −284988. | − | 493614.i | −0.462275 | − | 0.800684i | ||||
\(208\) | 172062. | − | 298020.i | 0.275757 | − | 0.477626i | ||||
\(209\) | 617206. | 0.977382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 776820. | 1.20120 | 0.600599 | − | 0.799551i | \(-0.294929\pi\) | ||||
0.600599 | + | 0.799551i | \(0.294929\pi\) | |||||||
\(212\) | 198100. | − | 343119.i | 0.302723 | − | 0.524331i | ||||
\(213\) | 445044. | + | 770838.i | 0.672130 | + | 1.16416i | ||||
\(214\) | 218188. | + | 377913.i | 0.325684 | + | 0.564101i | ||||
\(215\) | −50809.3 | + | 88004.3i | −0.0749630 | + | 0.129840i | ||||
\(216\) | −413669. | −0.603279 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 192060. | 0.273713 | ||||||||
\(219\) | −509184. | + | 881933.i | −0.717405 | + | 1.24258i | ||||
\(220\) | 297961. | + | 516084.i | 0.415053 | + | 0.718892i | ||||
\(221\) | 39312.0 | + | 68090.4i | 0.0541433 | + | 0.0937789i | ||||
\(222\) | 315497. | − | 546457.i | 0.429648 | − | 0.744173i | ||||
\(223\) | −81834.5 | −0.110198 | −0.0550990 | − | 0.998481i | \(-0.517547\pi\) | ||||
−0.0550990 | + | 0.998481i | \(0.517547\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 949071. | 1.24981 | ||||||||
\(226\) | −137422. | + | 238022.i | −0.178972 | + | 0.309989i | ||||
\(227\) | 376836. | + | 652699.i | 0.485386 | + | 0.840713i | 0.999859 | − | 0.0167932i | \(-0.00534570\pi\) |
−0.514473 | + | 0.857507i | \(0.672012\pi\) | |||||||
\(228\) | 760032. | + | 1.31641e6i | 0.968266 | + | 1.67709i | ||||
\(229\) | 13152.0 | − | 22779.9i | 0.0165730 | − | 0.0287053i | −0.857620 | − | 0.514284i | \(-0.828058\pi\) |
0.874193 | + | 0.485579i | \(0.161391\pi\) | |||||||
\(230\) | 224220. | 0.279483 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −523920. | −0.639065 | ||||||||
\(233\) | −23771.0 | + | 41172.6i | −0.0286852 | + | 0.0496842i | −0.880012 | − | 0.474952i | \(-0.842465\pi\) |
0.851326 | + | 0.524636i | \(0.175799\pi\) | |||||||
\(234\) | −199865. | − | 346176.i | −0.238615 | − | 0.413293i | ||||
\(235\) | −376272. | − | 651722.i | −0.444460 | − | 0.769827i | ||||
\(236\) | 523531. | − | 906782.i | 0.611874 | − | 1.05980i | ||||
\(237\) | 1.36431e6 | 1.57776 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.08899e6 | 1.23319 | 0.616595 | − | 0.787281i | \(-0.288512\pi\) | ||||
0.616595 | + | 0.787281i | \(0.288512\pi\) | |||||||
\(240\) | −614016. | + | 1.06351e6i | −0.688100 | + | 1.19182i | ||||
\(241\) | −674685. | − | 1.16859e6i | −0.748270 | − | 1.29604i | −0.948651 | − | 0.316323i | \(-0.897552\pi\) |
0.200382 | − | 0.979718i | \(-0.435782\pi\) | |||||||
\(242\) | −80395.0 | − | 139248.i | −0.0882451 | − | 0.152845i | ||||
\(243\) | −499662. | + | 865440.i | −0.542826 | + | 0.940203i | ||||
\(244\) | −996702. | −1.07174 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 471744. | 0.497014 | ||||||||
\(247\) | −570024. | + | 987311.i | −0.594498 | + | 1.02970i | ||||
\(248\) | −386690. | − | 669767.i | −0.399240 | − | 0.691504i | ||||
\(249\) | 6552.00 | + | 11348.4i | 0.00669693 | + | 0.0115994i | ||||
\(250\) | 47511.9 | − | 82293.1i | 0.0480787 | − | 0.0832748i | ||||
\(251\) | −630020. | −0.631205 | −0.315602 | − | 0.948892i | \(-0.602207\pi\) | ||||
−0.315602 | + | 0.948892i | \(0.602207\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −424864. | −0.417300 | ||||||||
\(254\) | 170368. | − | 295086.i | 0.165693 | − | 0.286988i | ||||
\(255\) | −140288. | − | 242985.i | −0.135104 | − | 0.234007i | ||||
\(256\) | 15232.0 | + | 26382.6i | 0.0145264 | + | 0.0251604i | ||||
\(257\) | −967025. | + | 1.67494e6i | −0.913282 | + | 1.58185i | −0.103886 | + | 0.994589i | \(0.533128\pi\) |
−0.809397 | + | 0.587262i | \(0.800206\pi\) | |||||||
\(258\) | −67745.7 | −0.0633626 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.10074e6 | −1.00983 | ||||||||
\(261\) | 831723. | − | 1.44059e6i | 0.755749 | − | 1.30900i | ||||
\(262\) | 348246. | + | 603180.i | 0.313425 | + | 0.542867i | ||||
\(263\) | 558560. | + | 967454.i | 0.497944 | + | 0.862464i | 0.999997 | − | 0.00237250i | \(-0.000755190\pi\) |
−0.502053 | + | 0.864837i | \(0.667422\pi\) | |||||||
\(264\) | −425659. | + | 737263.i | −0.375882 | + | 0.651048i | ||||
\(265\) | −1.06040e6 | −0.927588 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −509184. | −0.437116 | ||||||||
\(268\) | −51016.0 | + | 88362.3i | −0.0433880 | + | 0.0751502i | ||||
\(269\) | 760304. | + | 1.31688e6i | 0.640629 | + | 1.10960i | 0.985293 | + | 0.170875i | \(0.0546595\pi\) |
−0.344664 | + | 0.938726i | \(0.612007\pi\) | |||||||
\(270\) | 258336. | + | 447451.i | 0.215663 | + | 0.373539i | ||||
\(271\) | 510191. | − | 883677.i | 0.421997 | − | 0.730921i | −0.574137 | − | 0.818759i | \(-0.694662\pi\) |
0.996135 | + | 0.0878380i | \(0.0279958\pi\) | |||||||
\(272\) | 98321.2 | 0.0805796 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 151124. | 0.121607 | ||||||||
\(275\) | 353722. | − | 612664.i | 0.282053 | − | 0.488530i | ||||
\(276\) | −523181. | − | 906176.i | −0.413408 | − | 0.716044i | ||||
\(277\) | −948211. | − | 1.64235e6i | −0.742516 | − | 1.28607i | −0.951347 | − | 0.308123i | \(-0.900299\pi\) |
0.208831 | − | 0.977952i | \(-0.433034\pi\) | |||||||
\(278\) | −97047.3 | + | 168091.i | −0.0753132 | + | 0.130446i | ||||
\(279\) | 2.45548e6 | 1.88854 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.31911e6 | 0.996587 | 0.498293 | − | 0.867008i | \(-0.333960\pi\) | ||||
0.498293 | + | 0.867008i | \(0.333960\pi\) | |||||||
\(282\) | 250848. | − | 434481.i | 0.187840 | − | 0.325348i | ||||
\(283\) | 239396. | + | 414646.i | 0.177685 | + | 0.307759i | 0.941087 | − | 0.338164i | \(-0.109806\pi\) |
−0.763402 | + | 0.645923i | \(0.776473\pi\) | |||||||
\(284\) | 498848. | + | 864030.i | 0.367005 | + | 0.635672i | ||||
\(285\) | 2.03417e6 | − | 3.52329e6i | 1.48346 | − | 2.56942i | ||||
\(286\) | −297961. | −0.215400 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.96291e6 | −1.39450 | ||||||||
\(289\) | 698696. | − | 1.21018e6i | 0.492089 | − | 0.852324i | ||||
\(290\) | 327188. | + | 566706.i | 0.228456 | + | 0.395697i | ||||
\(291\) | −2.29320e6 | − | 3.97194e6i | −1.58748 | − | 2.74960i | ||||
\(292\) | −570743. | + | 988556.i | −0.391727 | + | 0.678491i | ||||
\(293\) | −1.50187e6 | −1.02203 | −0.511015 | − | 0.859572i | \(-0.670730\pi\) | ||||
−0.511015 | + | 0.859572i | \(0.670730\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.80238e6 | −1.87488 | ||||||||
\(296\) | 757800. | − | 1.31255e6i | 0.502719 | − | 0.870735i | ||||
\(297\) | −489508. | − | 847853.i | −0.322009 | − | 0.557737i | ||||
\(298\) | 361030. | + | 625322.i | 0.235506 | + | 0.407909i | ||||
\(299\) | 392386. | − | 679632.i | 0.253825 | − | 0.439639i | ||||
\(300\) | 1.74230e6 | 1.11769 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −64560.0 | −0.0407330 | ||||||||
\(303\) | −948168. | + | 1.64228e6i | −0.593306 | + | 1.02764i | ||||
\(304\) | 712829. | + | 1.23466e6i | 0.442386 | + | 0.766235i | ||||
\(305\) | 1.33380e6 | + | 2.31021e6i | 0.820996 | + | 1.42201i | ||||
\(306\) | 57104.3 | − | 98907.5i | 0.0348630 | − | 0.0603845i | ||||
\(307\) | 1.19657e6 | 0.724588 | 0.362294 | − | 0.932064i | \(-0.381994\pi\) | ||||
0.362294 | + | 0.932064i | \(0.381994\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −273312. | −0.162841 | ||||||||
\(310\) | −482976. | + | 836539.i | −0.285444 | + | 0.494404i | ||||
\(311\) | −657373. | − | 1.13860e6i | −0.385400 | − | 0.667532i | 0.606425 | − | 0.795141i | \(-0.292603\pi\) |
−0.991825 | + | 0.127609i | \(0.959270\pi\) | |||||||
\(312\) | −786240. | − | 1.36181e6i | −0.457266 | − | 0.792007i | ||||
\(313\) | −1.32636e6 | + | 2.29733e6i | −0.765247 | + | 1.32545i | 0.174869 | + | 0.984592i | \(0.444050\pi\) |
−0.940116 | + | 0.340854i | \(0.889284\pi\) | |||||||
\(314\) | −265737. | −0.152100 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.52925e6 | 0.861510 | ||||||||
\(317\) | 799961. | − | 1.38557e6i | 0.447116 | − | 0.774428i | −0.551080 | − | 0.834452i | \(-0.685784\pi\) |
0.998197 | + | 0.0600237i | \(0.0191176\pi\) | |||||||
\(318\) | −353467. | − | 612223.i | −0.196011 | − | 0.339501i | ||||
\(319\) | −619972. | − | 1.07382e6i | −0.341111 | − | 0.590821i | ||||
\(320\) | −400479. | + | 693650.i | −0.218628 | + | 0.378674i | ||||
\(321\) | −5.45033e6 | −2.95230 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −325728. | −0.173720 | ||||||||
\(324\) | −90594.0 | + | 156913.i | −0.0479443 | + | 0.0830419i | ||||
\(325\) | 653364. | + | 1.13166e6i | 0.343121 | + | 0.594302i | ||||
\(326\) | −61364.0 | − | 106286.i | −0.0319794 | − | 0.0553899i | ||||
\(327\) | −1.19941e6 | + | 2.07745e6i | −0.620297 | + | 1.07439i | ||||
\(328\) | 1.13309e6 | 0.581542 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.06330e6 | 0.537489 | ||||||||
\(331\) | 55854.0 | − | 96742.0i | 0.0280210 | − | 0.0485339i | −0.851675 | − | 0.524071i | \(-0.824413\pi\) |
0.879696 | + | 0.475537i | \(0.157746\pi\) | |||||||
\(332\) | 7344.12 | + | 12720.4i | 0.00365674 | + | 0.00633366i | ||||
\(333\) | 2.40602e6 | + | 4.16734e6i | 1.18902 | + | 2.05944i | ||||
\(334\) | −380845. | + | 659643.i | −0.186802 | + | 0.323551i | ||||
\(335\) | 273081. | 0.132947 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.59301e6 | 0.764087 | 0.382043 | − | 0.924144i | \(-0.375220\pi\) | ||||
0.382043 | + | 0.924144i | \(0.375220\pi\) | |||||||
\(338\) | −96109.0 | + | 166466.i | −0.0457586 | + | 0.0792561i | ||||
\(339\) | −1.71640e6 | − | 2.97289e6i | −0.811184 | − | 1.40501i | ||||
\(340\) | −157248. | − | 272362.i | −0.0737714 | − | 0.127776i | ||||
\(341\) | 915167. | − | 1.58512e6i | 0.426201 | − | 0.738202i | ||||
\(342\) | 1.65602e6 | 0.765599 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −162720. | −0.0741387 | ||||||||
\(345\) | −1.40026e6 | + | 2.42531e6i | −0.633373 | + | 1.09703i | ||||
\(346\) | −517311. | − | 896008.i | −0.232306 | − | 0.402366i | ||||
\(347\) | 1.66838e6 | + | 2.88972e6i | 0.743827 | + | 1.28835i | 0.950741 | + | 0.309987i | \(0.100325\pi\) |
−0.206914 | + | 0.978359i | \(0.566342\pi\) | |||||||
\(348\) | 1.52688e6 | − | 2.64463e6i | 0.675859 | − | 1.17062i | ||||
\(349\) | 1.60259e6 | 0.704303 | 0.352151 | − | 0.935943i | \(-0.385450\pi\) | ||||
0.352151 | + | 0.935943i | \(0.385450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.80835e6 | 0.783457 | ||||||||
\(352\) | −731584. | + | 1.26714e6i | −0.314708 | + | 0.545090i | ||||
\(353\) | 904825. | + | 1.56720e6i | 0.386481 | + | 0.669404i | 0.991973 | − | 0.126447i | \(-0.0403572\pi\) |
−0.605493 | + | 0.795851i | \(0.707024\pi\) | |||||||
\(354\) | −934128. | − | 1.61796e6i | −0.396185 | − | 0.686213i | ||||
\(355\) | 1.33513e6 | − | 2.31251e6i | 0.562280 | − | 0.973898i | ||||
\(356\) | −570743. | −0.238680 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.22113e6 | −0.503563 | ||||||||
\(359\) | −460396. | + | 797429.i | −0.188536 | + | 0.326555i | −0.944763 | − | 0.327756i | \(-0.893708\pi\) |
0.756226 | + | 0.654310i | \(0.227041\pi\) | |||||||
\(360\) | 1.71313e6 | + | 2.96722e6i | 0.696680 | + | 1.20669i | ||||
\(361\) | −1.12348e6 | − | 1.94592e6i | −0.453729 | − | 0.785882i | ||||
\(362\) | 433828. | − | 751411.i | 0.173999 | − | 0.301374i | ||||
\(363\) | 2.00827e6 | 0.799935 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.05510e6 | 1.20031 | ||||||||
\(366\) | −889200. | + | 1.54014e6i | −0.346974 | + | 0.600976i | ||||
\(367\) | 674010. | + | 1.16742e6i | 0.261217 | + | 0.452441i | 0.966566 | − | 0.256420i | \(-0.0825429\pi\) |
−0.705349 | + | 0.708861i | \(0.749210\pi\) | |||||||
\(368\) | −490688. | − | 849897.i | −0.188880 | − | 0.327150i | ||||
\(369\) | −1.79878e6 | + | 3.11559e6i | −0.687722 | + | 1.19117i | ||||
\(370\) | −1.89298e6 | −0.718857 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.50778e6 | 1.68890 | ||||||||
\(373\) | −1.56887e6 | + | 2.71736e6i | −0.583867 | + | 1.01129i | 0.411148 | + | 0.911568i | \(0.365128\pi\) |
−0.995016 | + | 0.0997192i | \(0.968206\pi\) | |||||||
\(374\) | −42565.9 | − | 73726.3i | −0.0157356 | − | 0.0272548i | ||||
\(375\) | 593424. | + | 1.02784e6i | 0.217915 | + | 0.377440i | ||||
\(376\) | 602517. | − | 1.04359e6i | 0.219786 | − | 0.380680i | ||||
\(377\) | 2.29032e6 | 0.829931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.83188e6 | −0.655088 | −0.327544 | − | 0.944836i | \(-0.606221\pi\) | ||||
−0.327544 | + | 0.944836i | \(0.606221\pi\) | |||||||
\(380\) | 2.28010e6 | − | 3.94924e6i | 0.810017 | − | 1.40299i | ||||
\(381\) | 2.12790e6 | + | 3.68562e6i | 0.750996 | + | 1.30076i | ||||
\(382\) | 341192. | + | 590962.i | 0.119630 | + | 0.207205i | ||||
\(383\) | −13863.9 | + | 24013.0i | −0.00482935 | + | 0.00836467i | −0.868430 | − | 0.495812i | \(-0.834871\pi\) |
0.863601 | + | 0.504177i | \(0.168204\pi\) | |||||||
\(384\) | −4.65227e6 | −1.61004 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.23232e6 | 0.420973 | ||||||||
\(387\) | 258318. | − | 447420.i | 0.0876753 | − | 0.151858i | ||||
\(388\) | −2.57044e6 | − | 4.45213e6i | −0.866819 | − | 1.50137i | ||||
\(389\) | 274171. | + | 474878.i | 0.0918645 | + | 0.159114i | 0.908296 | − | 0.418329i | \(-0.137384\pi\) |
−0.816431 | + | 0.577443i | \(0.804051\pi\) | |||||||
\(390\) | −982013. | + | 1.70090e6i | −0.326931 | + | 0.566261i | ||||
\(391\) | 224220. | 0.0741708 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.69918e6 | −2.84117 | ||||||||
\(394\) | 231478. | − | 400932.i | 0.0751224 | − | 0.130116i | ||||
\(395\) | −2.04646e6 | − | 3.54457e6i | −0.659950 | − | 1.14307i | ||||
\(396\) | −1.51486e6 | − | 2.62381e6i | −0.485438 | − | 0.840803i | ||||
\(397\) | −201926. | + | 349746.i | −0.0643007 | + | 0.111372i | −0.896384 | − | 0.443279i | \(-0.853815\pi\) |
0.832083 | + | 0.554651i | \(0.187148\pi\) | |||||||
\(398\) | −810251. | −0.256396 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.63410e6 | 0.510655 | ||||||||
\(401\) | 2.08214e6 | − | 3.60637e6i | 0.646619 | − | 1.11998i | −0.337306 | − | 0.941395i | \(-0.609516\pi\) |
0.983925 | − | 0.178582i | \(-0.0571509\pi\) | |||||||
\(402\) | 91027.1 | + | 157664.i | 0.0280935 | + | 0.0486593i | ||||
\(403\) | 1.69042e6 | + | 2.92789e6i | 0.518479 | + | 0.898032i | ||||
\(404\) | −1.06280e6 | + | 1.84082e6i | −0.323965 | + | 0.561123i | ||||
\(405\) | 484937. | 0.146909 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.58692e6 | 1.07334 | ||||||||
\(408\) | 224640. | − | 389088.i | 0.0668093 | − | 0.115717i | ||||
\(409\) | −1.27061e6 | − | 2.20076e6i | −0.375581 | − | 0.650525i | 0.614833 | − | 0.788657i | \(-0.289223\pi\) |
−0.990414 | + | 0.138133i | \(0.955890\pi\) | |||||||
\(410\) | −707616. | − | 1.22563e6i | −0.207892 | − | 0.360080i | ||||
\(411\) | −943769. | + | 1.63466e6i | −0.275589 | + | 0.477333i | ||||
\(412\) | −306355. | −0.0889163 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.13995e6 | −0.326878 | ||||||||
\(415\) | 19656.0 | − | 34045.2i | 0.00560241 | − | 0.00970366i | ||||
\(416\) | −1.35132e6 | − | 2.34055e6i | −0.382846 | − | 0.663109i | ||||
\(417\) | −1.21212e6 | − | 2.09945e6i | −0.341354 | − | 0.591243i | ||||
\(418\) | 617206. | − | 1.06903e6i | 0.172778 | − | 0.299261i | ||||
\(419\) | 2.30133e6 | 0.640389 | 0.320195 | − | 0.947352i | \(-0.396252\pi\) | ||||
0.320195 | + | 0.947352i | \(0.396252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.79991e6 | −0.769909 | −0.384955 | − | 0.922936i | \(-0.625783\pi\) | ||||
−0.384955 | + | 0.922936i | \(0.625783\pi\) | |||||||
\(422\) | 776820. | − | 1.34549e6i | 0.212344 | − | 0.367790i | ||||
\(423\) | 1.91299e6 | + | 3.31340e6i | 0.519831 | + | 0.900374i | ||||
\(424\) | −849000. | − | 1.47051e6i | −0.229347 | − | 0.397241i | ||||
\(425\) | −186675. | + | 323331.i | −0.0501320 | + | 0.0868312i | ||||
\(426\) | 1.78017e6 | 0.475268 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.10926e6 | −1.61205 | ||||||||
\(429\) | 1.86077e6 | − | 3.22294e6i | 0.488145 | − | 0.845492i | ||||
\(430\) | 101619. | + | 176009.i | 0.0265034 | + | 0.0459053i | ||||
\(431\) | −477160. | − | 826465.i | −0.123729 | − | 0.214305i | 0.797507 | − | 0.603310i | \(-0.206152\pi\) |
−0.921235 | + | 0.389006i | \(0.872819\pi\) | |||||||
\(432\) | 1.13069e6 | − | 1.95842e6i | 0.291498 | − | 0.504890i | ||||
\(433\) | −519334. | −0.133115 | −0.0665575 | − | 0.997783i | \(-0.521202\pi\) | ||||
−0.0665575 | + | 0.997783i | \(0.521202\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.17315e6 | −2.07093 | ||||||||
\(436\) | −1.34442e6 | + | 2.32860e6i | −0.338703 | + | 0.586650i | ||||
\(437\) | 1.62560e6 | + | 2.81562e6i | 0.407202 | + | 0.705294i | ||||
\(438\) | 1.01837e6 | + | 1.76387e6i | 0.253641 | + | 0.439319i | ||||
\(439\) | 2.99040e6 | − | 5.17953e6i | 0.740574 | − | 1.28271i | −0.211660 | − | 0.977343i | \(-0.567887\pi\) |
0.952234 | − | 0.305369i | \(-0.0987798\pi\) | |||||||
\(440\) | 2.55395e6 | 0.628900 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 157248. | 0.0382851 | ||||||||
\(443\) | −1.87410e6 | + | 3.24604e6i | −0.453716 | + | 0.785859i | −0.998613 | − | 0.0526438i | \(-0.983235\pi\) |
0.544898 | + | 0.838503i | \(0.316569\pi\) | |||||||
\(444\) | 4.41696e6 | + | 7.65040e6i | 1.06333 | + | 1.84173i | ||||
\(445\) | 763776. | + | 1.32290e6i | 0.182838 | + | 0.316684i | ||||
\(446\) | −81834.5 | + | 141741.i | −0.0194805 | + | 0.0337411i | ||||
\(447\) | −9.01853e6 | −2.13485 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 99458.0 | 0.0232822 | 0.0116411 | − | 0.999932i | \(-0.496294\pi\) | ||||
0.0116411 | + | 0.999932i | \(0.496294\pi\) | |||||||
\(450\) | 949071. | − | 1.64384e6i | 0.220936 | − | 0.382673i | ||||
\(451\) | 1.34083e6 | + | 2.32238e6i | 0.310407 | + | 0.537640i | ||||
\(452\) | −1.92391e6 | − | 3.33231e6i | −0.442933 | − | 0.767183i | ||||
\(453\) | 403177. | − | 698323.i | 0.0923103 | − | 0.159886i | ||||
\(454\) | 1.50734e6 | 0.343220 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.51456e6 | 1.46714 | ||||||||
\(457\) | 80907.0 | − | 140135.i | 0.0181216 | − | 0.0313875i | −0.856822 | − | 0.515612i | \(-0.827565\pi\) |
0.874944 | + | 0.484224i | \(0.160898\pi\) | |||||||
\(458\) | −26303.9 | − | 45559.7i | −0.00585945 | − | 0.0101489i | ||||
\(459\) | 258336. | + | 447451.i | 0.0572339 | + | 0.0991320i | ||||
\(460\) | −1.56954e6 | + | 2.71853e6i | −0.345843 | + | 0.599017i | ||||
\(461\) | 4.49198e6 | 0.984431 | 0.492215 | − | 0.870473i | \(-0.336187\pi\) | ||||
0.492215 | + | 0.870473i | \(0.336187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.59382e6 | 0.779118 | 0.389559 | − | 0.921001i | \(-0.372627\pi\) | ||||
0.389559 | + | 0.921001i | \(0.372627\pi\) | |||||||
\(464\) | 1.43205e6 | − | 2.48038e6i | 0.308790 | − | 0.534839i | ||||
\(465\) | −6.03237e6 | − | 1.04484e7i | −1.29377 | − | 2.24087i | ||||
\(466\) | 47542.0 | + | 82345.2i | 0.0101417 | + | 0.0175660i | ||||
\(467\) | 1.02612e6 | − | 1.77728e6i | 0.217723 | − | 0.377107i | −0.736389 | − | 0.676559i | \(-0.763470\pi\) |
0.954111 | + | 0.299452i | \(0.0968038\pi\) | |||||||
\(468\) | 5.59622e6 | 1.18108 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.50509e6 | −0.314280 | ||||||||
\(471\) | 1.65953e6 | − | 2.87439e6i | 0.344693 | − | 0.597026i | ||||
\(472\) | −2.24370e6 | − | 3.88621e6i | −0.463565 | − | 0.802918i | ||||
\(473\) | −192552. | − | 333510.i | −0.0395727 | − | 0.0685418i | ||||
\(474\) | 1.36431e6 | − | 2.36305e6i | 0.278911 | − | 0.483089i | ||||
\(475\) | −5.41359e6 | −1.10091 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.39115e6 | 1.08489 | ||||||||
\(478\) | 1.08899e6 | − | 1.88619e6i | 0.217999 | − | 0.377586i | ||||
\(479\) | −999924. | − | 1.73192e6i | −0.199126 | − | 0.344897i | 0.749119 | − | 0.662435i | \(-0.230477\pi\) |
−0.948245 | + | 0.317539i | \(0.897144\pi\) | |||||||
\(480\) | 4.82227e6 | + | 8.35242e6i | 0.955319 | + | 1.65466i | ||||
\(481\) | −3.31272e6 | + | 5.73780e6i | −0.652863 | + | 1.13079i | ||||
\(482\) | −2.69874e6 | −0.529107 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.25106e6 | 0.436791 | ||||||||
\(485\) | −6.87960e6 | + | 1.19158e7i | −1.32803 | + | 2.30022i | ||||
\(486\) | 999325. | + | 1.73088e6i | 0.191918 | + | 0.332412i | ||||
\(487\) | −1.08563e6 | − | 1.88036e6i | −0.207424 | − | 0.359269i | 0.743478 | − | 0.668760i | \(-0.233175\pi\) |
−0.950902 | + | 0.309491i | \(0.899841\pi\) | |||||||
\(488\) | −2.13579e6 | + | 3.69930e6i | −0.405984 | + | 0.703185i | ||||
\(489\) | 1.53287e6 | 0.289890 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.04555e6 | 0.570114 | 0.285057 | − | 0.958511i | \(-0.407987\pi\) | ||||
0.285057 | + | 0.958511i | \(0.407987\pi\) | |||||||
\(492\) | −3.30221e6 | + | 5.71959e6i | −0.615023 | + | 1.06525i | ||||
\(493\) | 327188. | + | 566706.i | 0.0606289 | + | 0.105012i | ||||
\(494\) | 1.14005e6 | + | 1.97462e6i | 0.210187 | + | 0.364054i | ||||
\(495\) | −4.05440e6 | + | 7.02243e6i | −0.743728 | + | 1.28817i | ||||
\(496\) | 4.22781e6 | 0.771635 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 26208.0 | 0.00473544 | ||||||||
\(499\) | 3.99613e6 | − | 6.92149e6i | 0.718436 | − | 1.24437i | −0.243184 | − | 0.969980i | \(-0.578192\pi\) |
0.961619 | − | 0.274387i | \(-0.0884748\pi\) | |||||||
\(500\) | 665167. | + | 1.15210e6i | 0.118989 | + | 0.206095i | ||||
\(501\) | −4.75675e6 | − | 8.23894e6i | −0.846674 | − | 1.46648i | ||||
\(502\) | −630020. | + | 1.09123e6i | −0.111582 | + | 0.193266i | ||||
\(503\) | −9.47811e6 | −1.67033 | −0.835164 | − | 0.550001i | \(-0.814627\pi\) | ||||
−0.835164 | + | 0.550001i | \(0.814627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.68901e6 | 0.992677 | ||||||||
\(506\) | −424864. | + | 735886.i | −0.0737690 | + | 0.127772i | ||||
\(507\) | −1.20040e6 | − | 2.07916e6i | −0.207399 | − | 0.359225i | ||||
\(508\) | 2.38515e6 | + | 4.13120e6i | 0.410069 | + | 0.710260i | ||||
\(509\) | 5.05017e6 | − | 8.74715e6i | 0.863995 | − | 1.49648i | −0.00404624 | − | 0.999992i | \(-0.501288\pi\) |
0.868041 | − | 0.496492i | \(-0.165379\pi\) | |||||||
\(510\) | −561151. | −0.0955331 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.89875e6 | −0.994455 | ||||||||
\(513\) | −3.74587e6 | + | 6.48804e6i | −0.628434 | + | 1.08848i | ||||
\(514\) | 1.93405e6 | + | 3.34987e6i | 0.322894 | + | 0.559269i | ||||
\(515\) | 409968. | + | 710085.i | 0.0681133 | + | 0.117976i | ||||
\(516\) | 474220. | − | 821373.i | 0.0784072 | − | 0.135805i | ||||
\(517\) | 2.85192e6 | 0.469257 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.29224e7 | 2.10584 | ||||||||
\(520\) | −2.35872e6 | + | 4.08542e6i | −0.382532 | + | 0.662565i | ||||
\(521\) | 2.55987e6 | + | 4.43383e6i | 0.413166 | + | 0.715624i | 0.995234 | − | 0.0975158i | \(-0.0310897\pi\) |
−0.582068 | + | 0.813140i | \(0.697756\pi\) | |||||||
\(522\) | −1.66345e6 | − | 2.88117e6i | −0.267198 | − | 0.462800i | ||||
\(523\) | 1.75738e6 | − | 3.04387e6i | 0.280939 | − | 0.486600i | −0.690678 | − | 0.723163i | \(-0.742688\pi\) |
0.971616 | + | 0.236563i | \(0.0760209\pi\) | |||||||
\(524\) | −9.75089e6 | −1.55137 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.23424e6 | 0.352100 | ||||||||
\(527\) | −482976. | + | 836539.i | −0.0757529 | + | 0.131208i | ||||
\(528\) | −2.32694e6 | − | 4.03037e6i | −0.363245 | − | 0.629159i | ||||
\(529\) | 2.09916e6 | + | 3.63586e6i | 0.326142 | + | 0.564895i | ||||
\(530\) | −1.06040e6 | + | 1.83667e6i | −0.163976 | + | 0.284015i | ||||
\(531\) | 1.42475e7 | 2.19282 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.95331e6 | −0.755227 | ||||||||
\(534\) | −509184. | + | 881933.i | −0.0772719 | + | 0.133839i | ||||
\(535\) | 8.17550e6 | + | 1.41604e7i | 1.23489 | + | 2.13890i | ||||
\(536\) | 218640. | + | 378696.i | 0.0328714 | + | 0.0569349i | ||||
\(537\) | 7.62594e6 | − | 1.32085e7i | 1.14119 | − | 1.97660i | ||||
\(538\) | 3.04121e6 | 0.452993 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.23341e6 | −1.06748 | ||||||||
\(541\) | 1.73774e6 | − | 3.00985e6i | 0.255265 | − | 0.442132i | −0.709703 | − | 0.704501i | \(-0.751171\pi\) |
0.964967 | + | 0.262370i | \(0.0845040\pi\) | |||||||
\(542\) | −1.02038e6 | − | 1.76735e6i | −0.149199 | − | 0.258420i | ||||
\(543\) | 5.41850e6 | + | 9.38512e6i | 0.788642 | + | 1.36597i | ||||
\(544\) | 386091. | − | 668729.i | 0.0559361 | − | 0.0968842i | ||||
\(545\) | 7.19649e6 | 1.03784 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.85765e6 | −1.12286 | −0.561429 | − | 0.827525i | \(-0.689748\pi\) | ||||
−0.561429 | + | 0.827525i | \(0.689748\pi\) | |||||||
\(548\) | −1.05787e6 | + | 1.83228e6i | −0.150480 | + | 0.260640i | ||||
\(549\) | −6.78113e6 | − | 1.17453e7i | −0.960221 | − | 1.66315i | ||||
\(550\) | −707444. | − | 1.22533e6i | −0.0997207 | − | 0.172721i | ||||
\(551\) | −4.74423e6 | + | 8.21724e6i | −0.665712 | + | 1.15305i | ||||
\(552\) | −4.48441e6 | −0.626408 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.79284e6 | −0.525038 | ||||||||
\(555\) | 1.18217e7 | − | 2.04758e7i | 1.62910 | − | 2.82168i | ||||
\(556\) | −1.35866e6 | − | 2.35327e6i | −0.186391 | − | 0.322838i | ||||
\(557\) | −4.53269e6 | − | 7.85084e6i | −0.619039 | − | 1.07221i | −0.989661 | − | 0.143423i | \(-0.954189\pi\) |
0.370623 | − | 0.928783i | \(-0.379144\pi\) | |||||||
\(558\) | 2.45548e6 | − | 4.25302e6i | 0.333850 | − | 0.578245i | ||||
\(559\) | 711330. | 0.0962813 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.06330e6 | 0.142642 | ||||||||
\(562\) | 1.31911e6 | − | 2.28477e6i | 0.176173 | − | 0.305141i | ||||
\(563\) | 2.90479e6 | + | 5.03124e6i | 0.386227 | + | 0.668966i | 0.991939 | − | 0.126719i | \(-0.0404446\pi\) |
−0.605711 | + | 0.795685i | \(0.707111\pi\) | |||||||
\(564\) | 3.51187e6 | + | 6.08274e6i | 0.464880 | + | 0.805196i | ||||
\(565\) | −5.14920e6 | + | 8.91868e6i | −0.678608 | + | 1.17538i | ||||
\(566\) | 957583. | 0.125642 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.27584e6 | 0.556097 | ||||||||
\(569\) | −5.27797e6 | + | 9.14171e6i | −0.683418 | + | 1.18371i | 0.290513 | + | 0.956871i | \(0.406174\pi\) |
−0.973931 | + | 0.226844i | \(0.927159\pi\) | |||||||
\(570\) | −4.06834e6 | − | 7.04657e6i | −0.524482 | − | 0.908429i | ||||
\(571\) | −3.99792e6 | − | 6.92460e6i | −0.513150 | − | 0.888801i | −0.999884 | − | 0.0152511i | \(-0.995145\pi\) |
0.486734 | − | 0.873550i | \(-0.338188\pi\) | |||||||
\(572\) | 2.08573e6 | − | 3.61259e6i | 0.266543 | − | 0.461667i | ||||
\(573\) | −8.52297e6 | −1.08444 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.72654e6 | 0.470041 | ||||||||
\(576\) | 2.03606e6 | − | 3.52657e6i | 0.255703 | − | 0.442890i | ||||
\(577\) | −1.30470e6 | − | 2.25982e6i | −0.163145 | − | 0.282575i | 0.772850 | − | 0.634588i | \(-0.218830\pi\) |
−0.935995 | + | 0.352014i | \(0.885497\pi\) | |||||||
\(578\) | −1.39739e6 | − | 2.42036e6i | −0.173980 | − | 0.301342i | ||||
\(579\) | −7.69581e6 | + | 1.33295e7i | −0.954021 | + | 1.65241i | ||||
\(580\) | −9.16126e6 | −1.13080 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.17280e6 | −1.12252 | ||||||||
\(583\) | 2.00930e6 | − | 3.48021e6i | 0.244835 | − | 0.424067i | ||||
\(584\) | 2.44604e6 | + | 4.23667e6i | 0.296778 | + | 0.514034i | ||||
\(585\) | −7.48894e6 | − | 1.29712e7i | −0.904754 | − | 1.56708i | ||||
\(586\) | −1.50187e6 | + | 2.60132e6i | −0.180671 | + | 0.312932i | ||||
\(587\) | −4.41749e6 | −0.529151 | −0.264576 | − | 0.964365i | \(-0.585232\pi\) | ||||
−0.264576 | + | 0.964365i | \(0.585232\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.40063e7 | −1.66355 | ||||||||
\(590\) | −2.80238e6 | + | 4.85387e6i | −0.331434 | + | 0.574061i | ||||
\(591\) | 2.89116e6 | + | 5.00763e6i | 0.340489 | + | 0.589745i | ||||
\(592\) | 4.14264e6 | + | 7.17526e6i | 0.485817 | + | 0.841460i | ||||
\(593\) | −2.77053e6 | + | 4.79870e6i | −0.323539 | + | 0.560386i | −0.981216 | − | 0.192915i | \(-0.938206\pi\) |
0.657677 | + | 0.753300i | \(0.271539\pi\) | |||||||
\(594\) | −1.95803e6 | −0.227695 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.01088e7 | −1.16570 | ||||||||
\(597\) | 5.06002e6 | − | 8.76420e6i | 0.581053 | − | 1.00641i | ||||
\(598\) | −784771. | − | 1.35926e6i | −0.0897409 | − | 0.155436i | ||||
\(599\) | −2.54306e6 | − | 4.40470e6i | −0.289594 | − | 0.501591i | 0.684119 | − | 0.729370i | \(-0.260187\pi\) |
−0.973713 | + | 0.227779i | \(0.926853\pi\) | |||||||
\(600\) | 3.73351e6 | − | 6.46663e6i | 0.423389 | − | 0.733331i | ||||
\(601\) | −2.41307e6 | −0.272511 | −0.136255 | − | 0.990674i | \(-0.543507\pi\) | ||||
−0.136255 | + | 0.990674i | \(0.543507\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.38836e6 | −0.155493 | ||||||||
\(604\) | 451920. | − | 782748.i | 0.0504045 | − | 0.0873031i | ||||
\(605\) | −3.01240e6 | − | 5.21763e6i | −0.334599 | − | 0.579542i | ||||
\(606\) | 1.89634e6 | + | 3.28455e6i | 0.209765 | + | 0.363324i | ||||
\(607\) | 3.81085e6 | − | 6.60058e6i | 0.419807 | − | 0.727127i | −0.576113 | − | 0.817370i | \(-0.695431\pi\) |
0.995920 | + | 0.0902430i | \(0.0287644\pi\) | |||||||
\(608\) | 1.11966e7 | 1.22837 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.33520e6 | 0.580532 | ||||||||
\(611\) | −2.63390e6 | + | 4.56206e6i | −0.285428 | + | 0.494376i | ||||
\(612\) | 799460. | + | 1.38470e6i | 0.0862816 | + | 0.149444i | ||||
\(613\) | −1.80063e6 | − | 3.11878e6i | −0.193541 | − | 0.335223i | 0.752880 | − | 0.658158i | \(-0.228664\pi\) |
−0.946421 | + | 0.322935i | \(0.895331\pi\) | |||||||
\(614\) | 1.19657e6 | − | 2.07251e6i | 0.128090 | − | 0.221859i | ||||
\(615\) | 1.76762e7 | 1.88453 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.22901e6 | 0.764480 | 0.382240 | − | 0.924063i | \(-0.375153\pi\) | ||||
0.382240 | + | 0.924063i | \(0.375153\pi\) | |||||||
\(618\) | −273312. | + | 473390.i | −0.0287864 | + | 0.0498595i | ||||
\(619\) | −6.29162e6 | − | 1.08974e7i | −0.659988 | − | 1.14313i | −0.980618 | − | 0.195928i | \(-0.937228\pi\) |
0.320630 | − | 0.947204i | \(-0.396105\pi\) | |||||||
\(620\) | −6.76166e6 | − | 1.17115e7i | −0.706439 | − | 1.22359i | ||||
\(621\) | 2.57853e6 | − | 4.46615e6i | 0.268314 | − | 0.464734i | ||||
\(622\) | −2.62949e6 | −0.272519 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.59622e6 | 0.883784 | ||||||||
\(625\) | 5.67246e6 | − | 9.82499e6i | 0.580860 | − | 1.00608i | ||||
\(626\) | 2.65273e6 | + | 4.59465e6i | 0.270556 | + | 0.468616i | ||||
\(627\) | 7.70890e6 | + | 1.33522e7i | 0.783111 | + | 1.35639i | ||||
\(628\) | 1.86016e6 | − | 3.22189e6i | 0.188214 | − | 0.325996i | ||||
\(629\) | −1.89298e6 | −0.190774 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.98350e6 | 0.598249 | 0.299125 | − | 0.954214i | \(-0.403305\pi\) | ||||
0.299125 | + | 0.954214i | \(0.403305\pi\) | |||||||
\(632\) | 3.27696e6 | − | 5.67586e6i | 0.326346 | − | 0.565248i | ||||
\(633\) | 9.70248e6 | + | 1.68052e7i | 0.962439 | + | 1.66699i | ||||
\(634\) | −1.59992e6 | − | 2.77115e6i | −0.158080 | − | 0.273802i | ||||
\(635\) | 6.38369e6 | − | 1.10569e7i | 0.628257 | − | 1.08817i | ||||
\(636\) | 9.89707e6 | 0.970206 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.47989e6 | −0.241202 | ||||||||
\(639\) | −6.78790e6 | + | 1.17570e7i | −0.657632 | + | 1.13905i | ||||
\(640\) | 6.97841e6 | + | 1.20870e7i | 0.673452 | + | 1.16645i | ||||
\(641\) | 3.87000e6 | + | 6.70304e6i | 0.372020 | + | 0.644357i | 0.989876 | − | 0.141934i | \(-0.0453320\pi\) |
−0.617856 | + | 0.786291i | \(0.711999\pi\) | |||||||
\(642\) | −5.45033e6 | + | 9.44026e6i | −0.521898 | + | 0.903954i | ||||
\(643\) | −6.81377e6 | −0.649920 | −0.324960 | − | 0.945728i | \(-0.605351\pi\) | ||||
−0.324960 | + | 0.945728i | \(0.605351\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.53843e6 | −0.240252 | ||||||||
\(646\) | −325728. | + | 564177.i | −0.0307096 | + | 0.0531905i | ||||
\(647\) | −5.35604e6 | − | 9.27692e6i | −0.503017 | − | 0.871251i | −0.999994 | − | 0.00348730i | \(-0.998890\pi\) |
0.496977 | − | 0.867764i | \(-0.334443\pi\) | |||||||
\(648\) | 388260. | + | 672486.i | 0.0363233 | + | 0.0629138i | ||||
\(649\) | 5.31010e6 | − | 9.19736e6i | 0.494870 | − | 0.857139i | ||||
\(650\) | 2.61346e6 | 0.242623 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.71819e6 | 0.158290 | ||||||||
\(653\) | −6.70834e6 | + | 1.16192e7i | −0.615647 | + | 1.06633i | 0.374623 | + | 0.927177i | \(0.377772\pi\) |
−0.990271 | + | 0.139155i | \(0.955561\pi\) | |||||||
\(654\) | 2.39883e6 | + | 4.15489e6i | 0.219308 | + | 0.379853i | ||||
\(655\) | 1.30488e7 | + | 2.26011e7i | 1.18841 | + | 2.05839i | ||||
\(656\) | −3.09712e6 | + | 5.36437e6i | −0.280995 | + | 0.486697i | ||||
\(657\) | −1.55324e7 | −1.40386 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.38574e7 | 1.24299 | 0.621494 | − | 0.783419i | \(-0.286526\pi\) | ||||
0.621494 | + | 0.783419i | \(0.286526\pi\) | |||||||
\(660\) | −7.44307e6 | + | 1.28918e7i | −0.665108 | + | 1.15200i | ||||
\(661\) | −6.03668e6 | − | 1.04558e7i | −0.537396 | − | 0.930797i | −0.999043 | − | 0.0437334i | \(-0.986075\pi\) |
0.461647 | − | 0.887064i | \(-0.347259\pi\) | |||||||
\(662\) | −111708. | − | 193484.i | −0.00990693 | − | 0.0171593i | ||||
\(663\) | −982013. | + | 1.70090e6i | −0.0867628 | + | 0.150278i | ||||
\(664\) | 62949.6 | 0.00554080 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.62406e6 | 0.840761 | ||||||||
\(667\) | 3.26577e6 | − | 5.65648e6i | 0.284231 | − | 0.492302i | ||||
\(668\) | −5.33183e6 | − | 9.23500e6i | −0.462312 | − | 0.800748i | ||||
\(669\) | −1.02211e6 | − | 1.77035e6i | −0.0882944 | − | 0.152930i | ||||
\(670\) | 273081. | − | 472991.i | 0.0235020 | − | 0.0407067i | ||||
\(671\) | −1.01094e7 | −0.866801 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.32490e6 | −0.453183 | −0.226592 | − | 0.973990i | \(-0.572758\pi\) | ||||
−0.226592 | + | 0.973990i | \(0.572758\pi\) | |||||||
\(674\) | 1.59301e6 | − | 2.75917e6i | 0.135073 | − | 0.233953i | ||||
\(675\) | 4.29354e6 | + | 7.43662e6i | 0.362707 | + | 0.628227i | ||||
\(676\) | −1.34553e6 | − | 2.33052e6i | −0.113247 | − | 0.196149i | ||||
\(677\) | −1.17259e7 | + | 2.03098e7i | −0.983274 | + | 1.70308i | −0.333903 | + | 0.942607i | \(0.608366\pi\) |
−0.649370 | + | 0.760472i | \(0.724967\pi\) | |||||||
\(678\) | −6.86560e6 | −0.573594 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.34784e6 | −0.111781 | ||||||||
\(681\) | −9.41335e6 | + | 1.63044e7i | −0.777815 | + | 1.34722i | ||||
\(682\) | −1.83033e6 | − | 3.17023e6i | −0.150685 | − | 0.260994i | ||||
\(683\) | −9.11349e6 | − | 1.57850e7i | −0.747538 | − | 1.29477i | −0.949000 | − | 0.315277i | \(-0.897903\pi\) |
0.201462 | − | 0.979496i | \(-0.435431\pi\) | |||||||
\(684\) | −1.15922e7 | + | 2.00782e7i | −0.947380 | + | 1.64091i | ||||
\(685\) | 5.66261e6 | 0.461095 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 657072. | 0.0531155 | ||||||||
\(688\) | 444768. | − | 770361.i | 0.0358230 | − | 0.0620473i | ||||
\(689\) | 3.71140e6 | + | 6.42834e6i | 0.297845 | + | 0.515882i | ||||
\(690\) | 2.80051e6 | + | 4.85063e6i | 0.223931 | + | 0.387860i | ||||
\(691\) | 3.80429e6 | − | 6.58922e6i | 0.303095 | − | 0.524976i | −0.673740 | − | 0.738968i | \(-0.735313\pi\) |
0.976835 | + | 0.213992i | \(0.0686468\pi\) | |||||||
\(692\) | 1.44847e7 | 1.14986 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.67353e6 | 0.525965 | ||||||||
\(695\) | −3.63636e6 | + | 6.29836e6i | −0.285565 | + | 0.494613i | ||||
\(696\) | −6.54376e6 | − | 1.13341e7i | −0.512040 | − | 0.886880i | ||||
\(697\) | −707616. | − | 1.22563e6i | −0.0551716 | − | 0.0955600i | ||||
\(698\) | 1.60259e6 | − | 2.77577e6i | 0.124504 | − | 0.215648i | ||||
\(699\) | −1.18760e6 | −0.0919341 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 314162. | 0.0241467 | 0.0120734 | − | 0.999927i | \(-0.496157\pi\) | ||||
0.0120734 | + | 0.999927i | \(0.496157\pi\) | |||||||
\(702\) | 1.80835e6 | − | 3.13216e6i | 0.138497 | − | 0.239884i | ||||
\(703\) | −1.37241e7 | − | 2.37709e7i | −1.04736 | − | 1.81408i | ||||
\(704\) | −1.51770e6 | − | 2.62873e6i | −0.115413 | − | 0.199900i | ||||
\(705\) | 9.39927e6 | − | 1.62800e7i | 0.712232 | − | 1.23362i | ||||
\(706\) | 3.61930e6 | 0.273283 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.61556e7 | 1.96102 | ||||||||
\(709\) | −1.24143e7 | + | 2.15021e7i | −0.927482 | + | 1.60645i | −0.139961 | + | 0.990157i | \(0.544698\pi\) |
−0.787521 | + | 0.616288i | \(0.788636\pi\) | |||||||
\(710\) | −2.67026e6 | − | 4.62503e6i | −0.198796 | − | 0.344325i | ||||
\(711\) | 1.04043e7 | + | 1.80209e7i | 0.771864 | + | 1.33691i | ||||
\(712\) | −1.22302e6 | + | 2.11833e6i | −0.0904136 | + | 0.156601i | ||||
\(713\) | 9.64148e6 | 0.710264 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.11646e7 | −0.816730 | ||||||||
\(716\) | 8.54790e6 | − | 1.48054e7i | 0.623127 | − | 1.07929i | ||||
\(717\) | 1.36015e7 | + | 2.35585e7i | 0.988073 | + | 1.71139i | ||||
\(718\) | 920792. | + | 1.59486e6i | 0.0666577 | + | 0.115455i | ||||
\(719\) | 8.59659e6 | − | 1.48897e7i | 0.620160 | − | 1.07415i | −0.369295 | − | 0.929312i | \(-0.620401\pi\) |
0.989456 | − | 0.144837i | \(-0.0462658\pi\) | |||||||
\(720\) | −1.87302e7 | −1.34651 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.49391e6 | −0.320835 | ||||||||
\(723\) | 1.68536e7 | − | 2.91913e7i | 1.19908 | − | 2.07686i | ||||
\(724\) | 6.07359e6 | + | 1.05198e7i | 0.430624 | + | 0.745863i | ||||
\(725\) | 5.43785e6 | + | 9.41864e6i | 0.384222 | + | 0.665492i | ||||
\(726\) | 2.00827e6 | − | 3.47842e6i | 0.141410 | − | 0.244929i | ||||
\(727\) | 2.12927e7 | 1.49415 | 0.747076 | − | 0.664739i | \(-0.231457\pi\) | ||||
0.747076 | + | 0.664739i | \(0.231457\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.33907e7 | −1.63014 | ||||||||
\(730\) | 3.05510e6 | − | 5.29160e6i | 0.212187 | − | 0.367519i | ||||
\(731\) | 101619. | + | 176009.i | 0.00703363 | + | 0.0121826i | ||||
\(732\) | −1.24488e7 | − | 2.15620e7i | −0.858716 | − | 1.48734i | ||||
\(733\) | −9.80121e6 | + | 1.69762e7i | −0.673783 | + | 1.16703i | 0.303040 | + | 0.952978i | \(0.401998\pi\) |
−0.976823 | + | 0.214048i | \(0.931335\pi\) | |||||||
\(734\) | 2.69604e6 | 0.184708 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.70739e6 | −0.524461 | ||||||||
\(737\) | −517448. | + | 896246.i | −0.0350912 | + | 0.0607797i | ||||
\(738\) | 3.59757e6 | + | 6.23117e6i | 0.243147 | + | 0.421142i | ||||
\(739\) | −7.20905e6 | − | 1.24864e7i | −0.485587 | − | 0.841061i | 0.514276 | − | 0.857625i | \(-0.328061\pi\) |
−0.999863 | + | 0.0165639i | \(0.994727\pi\) | |||||||
\(740\) | 1.32509e7 | − | 2.29512e7i | 0.889540 | − | 1.54073i | ||||
\(741\) | −2.84784e7 | −1.90533 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.57521e6 | 0.370501 | 0.185250 | − | 0.982691i | \(-0.440690\pi\) | ||||
0.185250 | + | 0.982691i | \(0.440690\pi\) | |||||||
\(744\) | 9.65952e6 | − | 1.67308e7i | 0.639769 | − | 1.10811i | ||||
\(745\) | 1.35278e7 | + | 2.34308e7i | 0.892969 | + | 1.54667i | ||||
\(746\) | 3.13773e6 | + | 5.43471e6i | 0.206428 | + | 0.357544i | ||||
\(747\) | −99932.5 | + | 173088.i | −0.00655247 | + | 0.0113492i | ||||
\(748\) | 1.19185e6 | 0.0778872 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.37370e6 | 0.154089 | ||||||||
\(751\) | −254400. | + | 440634.i | −0.0164595 | + | 0.0285087i | −0.874138 | − | 0.485678i | \(-0.838573\pi\) |
0.857678 | + | 0.514187i | \(0.171906\pi\) | |||||||
\(752\) | 3.29376e6 | + | 5.70496e6i | 0.212397 | + | 0.367882i | ||||
\(753\) | −7.86895e6 | − | 1.36294e7i | −0.505743 | − | 0.875972i | ||||
\(754\) | 2.29032e6 | − | 3.96694e6i | 0.146712 | − | 0.254113i | ||||
\(755\) | −2.41906e6 | −0.154447 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.10466e7 | 0.700631 | 0.350316 | − | 0.936632i | \(-0.386074\pi\) | ||||
0.350316 | + | 0.936632i | \(0.386074\pi\) | |||||||
\(758\) | −1.83188e6 | + | 3.17292e6i | −0.115804 | + | 0.200579i | ||||
\(759\) | −5.30655e6 | − | 9.19121e6i | −0.334355 | − | 0.579120i | ||||
\(760\) | −9.77184e6 | − | 1.69253e7i | −0.613681 | − | 1.06293i | ||||
\(761\) | −3.38586e6 | + | 5.86449e6i | −0.211937 | + | 0.367086i | −0.952321 | − | 0.305098i | \(-0.901311\pi\) |
0.740383 | + | 0.672185i | \(0.234644\pi\) | |||||||
\(762\) | 8.51158e6 | 0.531035 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9.55338e6 | −0.592139 | ||||||||
\(765\) | 2.13970e6 | − | 3.70606e6i | 0.132190 | − | 0.228960i | ||||
\(766\) | 27727.8 | + | 48025.9i | 0.00170743 | + | 0.00295736i | ||||
\(767\) | 9.80834e6 | + | 1.69886e7i | 0.602015 | + | 1.04272i | ||||
\(768\) | −380495. | + | 659037.i | −0.0232780 | + | 0.0403187i | ||||
\(769\) | 2.48053e7 | 1.51261 | 0.756307 | − | 0.654216i | \(-0.227001\pi\) | ||||
0.756307 | + | 0.654216i | \(0.227001\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.83126e7 | −2.92701 | ||||||||
\(772\) | −8.62621e6 | + | 1.49410e7i | −0.520927 | + | 0.902272i | ||||
\(773\) | −8.14759e6 | − | 1.41120e7i | −0.490434 | − | 0.849456i | 0.509506 | − | 0.860467i | \(-0.329828\pi\) |
−0.999939 | + | 0.0110113i | \(0.996495\pi\) | |||||||
\(774\) | −516636. | − | 894840.i | −0.0309979 | − | 0.0536899i | ||||
\(775\) | −8.02705e6 | + | 1.39033e7i | −0.480067 | + | 0.831500i | ||||
\(776\) | −2.20324e7 | −1.31343 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.09668e6 | 0.0649580 | ||||||||
\(779\) | 1.02604e7 | − | 1.77716e7i | 0.605790 | − | 1.04926i | ||||
\(780\) | −1.37482e7 | − | 2.38126e7i | −0.809113 | − | 1.40142i | ||||
\(781\) | 5.05974e6 | + | 8.76373e6i | 0.296825 | + | 0.514117i | ||||
\(782\) | 224220. | − | 388361.i | 0.0131117 | − | 0.0227101i | ||||
\(783\) | 1.50506e7 | 0.877305 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.95717e6 | −0.576716 | ||||||||
\(786\) | −8.69918e6 | + | 1.50674e7i | −0.502253 | + | 0.869927i | ||||
\(787\) | −7.21069e6 | − | 1.24893e7i | −0.414992 | − | 0.718787i | 0.580436 | − | 0.814306i | \(-0.302882\pi\) |
−0.995428 | + | 0.0955188i | \(0.969549\pi\) | |||||||
\(788\) | 3.24069e6 | + | 5.61304e6i | 0.185918 | + | 0.322020i | ||||
\(789\) | −1.39528e7 | + | 2.41670e7i | −0.797939 | + | 1.38207i | ||||
\(790\) | −8.18584e6 | −0.466655 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.29845e7 | −0.735549 | ||||||||
\(793\) | 9.33660e6 | − | 1.61715e7i | 0.527237 | − | 0.913201i | ||||
\(794\) | 403852. | + | 699491.i | 0.0227337 | + | 0.0393760i | ||||
\(795\) | −1.32444e7 | − | 2.29400e7i | −0.743215 | − | 1.28729i | ||||
\(796\) | 5.67176e6 | − | 9.82377e6i | 0.317274 | − | 0.549535i | ||||
\(797\) | 1.10109e6 | 0.0614014 | 0.0307007 | − | 0.999529i | \(-0.490226\pi\) | ||||
0.0307007 | + | 0.999529i | \(0.490226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.50509e6 | −0.0834055 | ||||||||
\(800\) | 6.41682e6 | − | 1.11143e7i | 0.354482 | − | 0.613981i | ||||
\(801\) | −3.88309e6 | − | 6.72571e6i | −0.213844 | − | 0.370388i | ||||
\(802\) | −4.16427e6 | − | 7.21273e6i | −0.228614 | − | 0.395972i | ||||
\(803\) | −5.78896e6 | + | 1.00268e7i | −0.316820 | + | 0.548748i | ||||
\(804\) | −2.54876e6 | −0.139056 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.76166e6 | 0.366620 | ||||||||
\(807\) | −1.89924e7 | + | 3.28958e7i | −1.02659 | + | 1.77810i | ||||
\(808\) | 4.55485e6 | + | 7.88923e6i | 0.245440 | + | 0.425115i | ||||
\(809\) | 1.22573e7 | + | 2.12302e7i | 0.658450 | + | 1.14047i | 0.981017 | + | 0.193922i | \(0.0621208\pi\) |
−0.322567 | + | 0.946547i | \(0.604546\pi\) | |||||||
\(810\) | 484937. | − | 839935.i | 0.0259700 | − | 0.0449814i | ||||
\(811\) | −3.03580e7 | −1.62077 | −0.810383 | − | 0.585900i | \(-0.800741\pi\) | ||||
−0.810383 | + | 0.585900i | \(0.800741\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.54892e7 | 1.35247 | ||||||||
\(814\) | 3.58692e6 | − | 6.21273e6i | 0.189741 | − | 0.328641i | ||||
\(815\) | −2.29931e6 | − | 3.98252e6i | −0.121256 | − | 0.210022i | ||||
\(816\) | 1.22803e6 | + | 2.12701e6i | 0.0645631 | + | 0.111827i | ||||
\(817\) | −1.47347e6 | + | 2.55212e6i | −0.0772300 | + | 0.133766i | ||||
\(818\) | −5.08243e6 | −0.265576 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.98132e7 | 1.02901 | ||||||||
\(821\) | 1.27299e7 | − | 2.20489e7i | 0.659126 | − | 1.14164i | −0.321716 | − | 0.946836i | \(-0.604260\pi\) |
0.980842 | − | 0.194804i | \(-0.0624072\pi\) | |||||||
\(822\) | 1.88754e6 | + | 3.26931e6i | 0.0974353 | + | 0.168763i | ||||
\(823\) | −2.97616e6 | − | 5.15486e6i | −0.153164 | − | 0.265288i | 0.779225 | − | 0.626744i | \(-0.215613\pi\) |
−0.932389 | + | 0.361456i | \(0.882280\pi\) | |||||||
\(824\) | −656474. | + | 1.13705e6i | −0.0336821 | + | 0.0583392i | ||||
\(825\) | 1.76719e7 | 0.903961 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.85900e6 | −0.399580 | −0.199790 | − | 0.979839i | \(-0.564026\pi\) | ||||
−0.199790 | + | 0.979839i | \(0.564026\pi\) | |||||||
\(828\) | 7.97966e6 | − | 1.38212e7i | 0.404491 | − | 0.700599i | ||||
\(829\) | 5.63208e6 | + | 9.75504e6i | 0.284631 | + | 0.492995i | 0.972520 | − | 0.232821i | \(-0.0747956\pi\) |
−0.687889 | + | 0.725816i | \(0.741462\pi\) | |||||||
\(830\) | −39312.0 | − | 68090.4i | −0.00198075 | − | 0.00343076i | ||||
\(831\) | 2.36863e7 | − | 4.10259e7i | 1.18986 | − | 2.06089i | ||||
\(832\) | 5.60671e6 | 0.280802 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.84848e6 | −0.241374 | ||||||||
\(835\) | −1.42703e7 | + | 2.47168e7i | −0.708297 | + | 1.22681i | ||||
\(836\) | 8.64088e6 | + | 1.49664e7i | 0.427604 | + | 0.740633i | ||||
\(837\) | 1.11084e7 | + | 1.92404e7i | 0.548075 | + | 0.949293i | ||||
\(838\) | 2.30133e6 | − | 3.98602e6i | 0.113206 | − | 0.196078i | ||||
\(839\) | 7.80470e6 | 0.382782 | 0.191391 | − | 0.981514i | \(-0.438700\pi\) | ||||
0.191391 | + | 0.981514i | \(0.438700\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.44919e6 | −0.0706539 | ||||||||
\(842\) | −2.79991e6 | + | 4.84959e6i | −0.136102 | + | 0.235736i | ||||
\(843\) | 1.64757e7 | + | 2.85367e7i | 0.798499 | + | 1.38304i | ||||
\(844\) | 1.08755e7 | + | 1.88369e7i | 0.525524 | + | 0.910234i | ||||
\(845\) | −3.60120e6 | + | 6.23747e6i | −0.173503 | + | 0.300515i | ||||
\(846\) | 7.65197e6 | 0.367576 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.28240e6 | 0.443272 | ||||||||
\(849\) | −5.98010e6 | + | 1.03578e7i | −0.284734 | + | 0.493174i | ||||
\(850\) | 373351. | + | 646663.i | 0.0177243 | + | 0.0306994i | ||||
\(851\) | 9.44724e6 | + | 1.63631e7i | 0.447179 | + | 0.774536i | ||||
\(852\) | −1.24612e7 | + | 2.15835e7i | −0.588114 | + | 1.01864i | ||||
\(853\) | −1.50581e7 | −0.708593 | −0.354296 | − | 0.935133i | \(-0.615280\pi\) | ||||
−0.354296 | + | 0.935133i | \(0.615280\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.20512e7 | 2.90292 | ||||||||
\(856\) | −1.30913e7 | + | 2.26748e7i | −0.610658 | + | 1.05769i | ||||
\(857\) | 1.14368e7 | + | 1.98091e7i | 0.531928 | + | 0.921327i | 0.999305 | + | 0.0372686i | \(0.0118657\pi\) |
−0.467377 | + | 0.884058i | \(0.654801\pi\) | |||||||
\(858\) | −3.72154e6 | − | 6.44589e6i | −0.172585 | − | 0.298927i | ||||
\(859\) | 4.11432e6 | − | 7.12621e6i | 0.190246 | − | 0.329515i | −0.755086 | − | 0.655626i | \(-0.772405\pi\) |
0.945332 | + | 0.326111i | \(0.105738\pi\) | |||||||
\(860\) | −2.84532e6 | −0.131185 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.90864e6 | −0.0874895 | ||||||||
\(863\) | −2.04951e6 | + | 3.54985e6i | −0.0936748 | + | 0.162249i | −0.909055 | − | 0.416677i | \(-0.863195\pi\) |
0.815380 | + | 0.578926i | \(0.196528\pi\) | |||||||
\(864\) | −8.88009e6 | − | 1.53808e7i | −0.404700 | − | 0.700960i | ||||
\(865\) | −1.93836e7 | − | 3.35734e7i | −0.880835 | − | 1.52565i | ||||
\(866\) | −519334. | + | 899513.i | −0.0235316 | + | 0.0407580i | ||||
\(867\) | 3.49069e7 | 1.57711 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.55109e7 | 0.696769 | ||||||||
\(870\) | −8.17315e6 | + | 1.41563e7i | −0.366093 | + | 0.634092i | ||||
\(871\) | −955784. | − | 1.65547e6i | −0.0426889 | − | 0.0739393i | ||||
\(872\) | 5.76180e6 | + | 9.97973e6i | 0.256606 | + | 0.444455i | ||||
\(873\) | 3.49764e7 | − | 6.05808e7i | 1.55324 | − | 2.69029i | ||||
\(874\) | 6.50239e6 | 0.287935 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.85143e7 | −1.25546 | ||||||||
\(877\) | −393889. | + | 682236.i | −0.0172932 | + | 0.0299527i | −0.874542 | − | 0.484949i | \(-0.838838\pi\) |
0.857249 | + | 0.514902i | \(0.172172\pi\) | |||||||
\(878\) | −5.98081e6 | − | 1.03591e7i | −0.261833 | − | 0.453507i | ||||
\(879\) | −1.87584e7 | − | 3.24905e7i | −0.818885 | − | 1.41835i | ||||
\(880\) | −6.98081e6 | + | 1.20911e7i | −0.303878 | + | 0.526332i | ||||
\(881\) | −1.73321e7 | −0.752336 | −0.376168 | − | 0.926551i | \(-0.622758\pi\) | ||||
−0.376168 | + | 0.926551i | \(0.622758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.23991e7 | 0.535164 | 0.267582 | − | 0.963535i | \(-0.413775\pi\) | ||||
0.267582 | + | 0.963535i | \(0.413775\pi\) | |||||||
\(884\) | −1.10074e6 | + | 1.90653e6i | −0.0473754 | + | 0.0820565i | ||||
\(885\) | −3.50018e7 | − | 6.06248e7i | −1.50221 | − | 2.60191i | ||||
\(886\) | 3.74820e6 | + | 6.49208e6i | 0.160413 | + | 0.277843i | ||||
\(887\) | −8.37776e6 | + | 1.45107e7i | −0.357535 | + | 0.619270i | −0.987548 | − | 0.157315i | \(-0.949716\pi\) |
0.630013 | + | 0.776585i | \(0.283050\pi\) | |||||||
\(888\) | 3.78597e7 | 1.61118 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.05510e6 | 0.129286 | ||||||||
\(891\) | −918882. | + | 1.59155e6i | −0.0387762 | + | 0.0671624i | ||||
\(892\) | −1.14568e6 | − | 1.98438e6i | −0.0482117 | − | 0.0835050i | ||||
\(893\) | −1.09119e7 | − | 1.88999e7i | −0.457901 | − | 0.793107i | ||||
\(894\) | −9.01853e6 | + | 1.56205e7i | −0.377391 | + | 0.653661i | ||||
\(895\) | −4.57557e7 | −1.90936 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.96036e7 | 0.813494 | ||||||||
\(898\) | 99458.0 | − | 172266.i | 0.00411575 | − | 0.00712869i | ||||
\(899\) | 1.40691e7 | + | 2.43684e7i | 0.580586 | + | 1.00560i | ||||
\(900\) | 1.32870e7 | + | 2.30137e7i | 0.546790 | + | 0.947068i | ||||
\(901\) | −1.06040e6 | + | 1.83667e6i | −0.0435169 | + | 0.0753735i | ||||
\(902\) | 5.36330e6 | 0.219491 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.64906e7 | −0.671145 | ||||||||
\(905\) | 1.62555e7 | − | 2.81554e7i | 0.659750 | − | 1.14272i | ||||
\(906\) | −806354. | − | 1.39665e6i | −0.0326366 | − | 0.0565283i | ||||
\(907\) | 1.98271e7 | + | 3.43416e7i | 0.800280 | + | 1.38613i | 0.919432 | + | 0.393249i | \(0.128649\pi\) |
−0.119152 | + | 0.992876i | \(0.538018\pi\) | |||||||
\(908\) | −1.05514e7 | + | 1.82756e7i | −0.424713 | + | 0.735624i | ||||
\(909\) | −2.89233e7 | −1.16102 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.99138e7 | 1.19419 | 0.597097 | − | 0.802169i | \(-0.296321\pi\) | ||||
0.597097 | + | 0.802169i | \(0.296321\pi\) | |||||||
\(912\) | −1.78065e7 | + | 3.08417e7i | −0.708909 | + | 1.22787i | ||||
\(913\) | 74490.3 | + | 129021.i | 0.00295749 | + | 0.00512252i | ||||
\(914\) | −161814. | − | 280270.i | −0.00640694 | − | 0.0110971i | ||||
\(915\) | −3.33183e7 | + | 5.77090e7i | −1.31562 | + | 2.27872i | ||||
\(916\) | 736510. | 0.0290028 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.03334e6 | 0.0404705 | ||||||||
\(919\) | −9.94985e6 | + | 1.72336e7i | −0.388622 | + | 0.673113i | −0.992264 | − | 0.124142i | \(-0.960382\pi\) |
0.603642 | + | 0.797255i | \(0.293716\pi\) | |||||||
\(920\) | 6.72661e6 | + | 1.16508e7i | 0.262015 | + | 0.453824i | ||||
\(921\) | 1.49451e7 | + | 2.58857e7i | 0.580564 | + | 1.00557i | ||||
\(922\) | 4.49198e6 | − | 7.78033e6i | 0.174024 | − | 0.301419i | ||||
\(923\) | −1.86918e7 | −0.722183 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.14613e7 | −1.20899 | ||||||||
\(926\) | 3.59382e6 | − | 6.22467e6i | 0.137730 | − | 0.238555i | ||||
\(927\) | −2.08431e6 | − | 3.61012e6i | −0.0796640 | − | 0.137982i | ||||
\(928\) | −1.12468e7 | − | 1.94801e7i | −0.428706 | − | 0.742541i | ||||
\(929\) | 5.98313e6 | − | 1.03631e7i | 0.227452 | − | 0.393958i | −0.729600 | − | 0.683874i | \(-0.760294\pi\) |
0.957052 | + | 0.289916i | \(0.0936273\pi\) | |||||||
\(930\) | −2.41295e7 | −0.914830 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.33118e6 | −0.0501991 | ||||||||
\(933\) | 1.64212e7 | − | 2.84423e7i | 0.617590 | − | 1.06970i | ||||
\(934\) | −2.05223e6 | − | 3.55457e6i | −0.0769767 | − | 0.133327i | ||||
\(935\) | −1.59494e6 | − | 2.76252e6i | −0.0596646 | − | 0.103342i | ||||
\(936\) | 1.19919e7 | − | 2.07706e7i | 0.447402 | − | 0.774923i | ||||
\(937\) | 6.18165e6 | 0.230015 | 0.115007 | − | 0.993365i | \(-0.463311\pi\) | ||||
0.115007 | + | 0.993365i | \(0.463311\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.62651e7 | −2.45257 | ||||||||
\(940\) | 1.05356e7 | − | 1.82482e7i | 0.388902 | − | 0.673598i | ||||
\(941\) | −1.49713e7 | − | 2.59311e7i | −0.551171 | − | 0.954656i | −0.998190 | − | 0.0601315i | \(-0.980848\pi\) |
0.447020 | − | 0.894524i | \(-0.352485\pi\) | |||||||
\(942\) | −3.31906e6 | − | 5.74877e6i | −0.121867 | − | 0.211080i | ||||
\(943\) | −7.06294e6 | + | 1.22334e7i | −0.258646 | + | 0.447989i | ||||
\(944\) | 2.45312e7 | 0.895959 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −770208. | −0.0279821 | ||||||||
\(947\) | 2.42139e7 | − | 4.19398e7i | 0.877386 | − | 1.51968i | 0.0231865 | − | 0.999731i | \(-0.492619\pi\) |
0.854199 | − | 0.519946i | \(-0.174048\pi\) | |||||||
\(948\) | 1.91003e7 | + | 3.30827e7i | 0.690271 | + | 1.19558i | ||||
\(949\) | −1.06929e7 | − | 1.85206e7i | −0.385415 | − | 0.667558i | ||||
\(950\) | −5.41359e6 | + | 9.37661e6i | −0.194615 | + | 0.337083i | ||||
\(951\) | 3.99660e7 | 1.43298 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.26780e7 | 0.808860 | 0.404430 | − | 0.914569i | \(-0.367470\pi\) | ||||
0.404430 | + | 0.914569i | \(0.367470\pi\) | |||||||
\(954\) | 5.39115e6 | − | 9.33775e6i | 0.191783 | − | 0.332178i | ||||
\(955\) | 1.27845e7 | + | 2.21433e7i | 0.453601 | + | 0.785660i | ||||
\(956\) | 1.52459e7 | + | 2.64067e7i | 0.539521 | + | 0.934477i | ||||
\(957\) | 1.54869e7 | − | 2.68241e7i | 0.546619 | − | 0.946771i | ||||
\(958\) | −3.99970e6 | −0.140803 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.00079e7 | −0.700687 | ||||||||
\(961\) | −6.45339e6 | + | 1.11776e7i | −0.225413 | + | 0.390427i | ||||
\(962\) | 6.62544e6 | + | 1.14756e7i | 0.230822 | + | 0.399795i | ||||
\(963\) | −4.15648e7 | − | 7.19924e7i | −1.44431 | − | 2.50162i | ||||
\(964\) | 1.88912e7 | − | 3.27205e7i | 0.654736 | − | 1.13404i | ||||
\(965\) | 4.61749e7 | 1.59620 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.60431e6 | −0.123953 | −0.0619764 | − | 0.998078i | \(-0.519740\pi\) | ||||
−0.0619764 | + | 0.998078i | \(0.519740\pi\) | |||||||
\(968\) | 4.82370e6 | − | 8.35489e6i | 0.165460 | − | 0.286584i | ||||
\(969\) | −4.06834e6 | − | 7.04657e6i | −0.139190 | − | 0.241084i | ||||
\(970\) | 1.37592e7 | + | 2.38316e7i | 0.469531 | + | 0.813251i | ||||
\(971\) | 1.45403e7 | − | 2.51846e7i | 0.494910 | − | 0.857210i | −0.505072 | − | 0.863077i | \(-0.668534\pi\) |
0.999983 | + | 0.00586710i | \(0.00186757\pi\) | |||||||
\(972\) | −2.79811e7 | −0.949946 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.34251e6 | −0.146671 | ||||||||
\(975\) | −1.63210e7 | + | 2.82689e7i | −0.549840 | + | 0.952350i | ||||
\(976\) | −1.16756e7 | − | 2.02228e7i | −0.392334 | − | 0.679543i | ||||
\(977\) | 9.09799e6 | + | 1.57582e7i | 0.304936 | + | 0.528165i | 0.977247 | − | 0.212104i | \(-0.0680315\pi\) |
−0.672311 | + | 0.740269i | \(0.734698\pi\) | |||||||
\(978\) | 1.53287e6 | − | 2.65501e6i | 0.0512459 | − | 0.0887604i | ||||
\(979\) | −5.78896e6 | −0.193039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.65874e7 | −1.21383 | ||||||||
\(982\) | 3.04555e6 | − | 5.27504e6i | 0.100783 | − | 0.174561i | ||||
\(983\) | −1.66404e6 | − | 2.88221e6i | −0.0549263 | − | 0.0951352i | 0.837255 | − | 0.546813i | \(-0.184159\pi\) |
−0.892181 | + | 0.451678i | \(0.850826\pi\) | |||||||
\(984\) | 1.41523e7 | + | 2.45125e7i | 0.465951 | + | 0.807050i | ||||
\(985\) | 8.67348e6 | − | 1.50229e7i | 0.284841 | − | 0.493359i | ||||
\(986\) | 1.30875e6 | 0.0428711 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.19213e7 | −1.04037 | ||||||||
\(989\) | 1.01429e6 | − | 1.75680e6i | 0.0329739 | − | 0.0571125i | ||||
\(990\) | 8.10881e6 | + | 1.40449e7i | 0.262947 | + | 0.455438i | ||||
\(991\) | −2.62710e7 | − | 4.55027e7i | −0.849753 | − | 1.47182i | −0.881429 | − | 0.472317i | \(-0.843418\pi\) |
0.0316758 | − | 0.999498i | \(-0.489916\pi\) | |||||||
\(992\) | 1.66019e7 | − | 2.87553e7i | 0.535647 | − | 0.927768i | ||||
\(993\) | 2.79046e6 | 0.0898056 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.03601e7 | −0.972177 | ||||||||
\(996\) | −183456. | + | 317755.i | −0.00585981 | + | 0.0101495i | ||||
\(997\) | 614995. | + | 1.06520e6i | 0.0195945 | + | 0.0339386i | 0.875656 | − | 0.482935i | \(-0.160429\pi\) |
−0.856062 | + | 0.516873i | \(0.827096\pi\) | |||||||
\(998\) | −7.99225e6 | − | 1.38430e7i | −0.254005 | − | 0.439950i | ||||
\(999\) | −2.17693e7 | + | 3.77056e7i | −0.690130 | + | 1.19534i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 49.6.c.g.30.2 | 4 | ||
7.2 | even | 3 | 49.6.a.c.1.1 | ✓ | 2 | ||
7.3 | odd | 6 | inner | 49.6.c.g.18.1 | 4 | ||
7.4 | even | 3 | inner | 49.6.c.g.18.2 | 4 | ||
7.5 | odd | 6 | 49.6.a.c.1.2 | yes | 2 | ||
7.6 | odd | 2 | inner | 49.6.c.g.30.1 | 4 | ||
21.2 | odd | 6 | 441.6.a.u.1.2 | 2 | |||
21.5 | even | 6 | 441.6.a.u.1.1 | 2 | |||
28.19 | even | 6 | 784.6.a.z.1.1 | 2 | |||
28.23 | odd | 6 | 784.6.a.z.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.6.a.c.1.1 | ✓ | 2 | 7.2 | even | 3 | ||
49.6.a.c.1.2 | yes | 2 | 7.5 | odd | 6 | ||
49.6.c.g.18.1 | 4 | 7.3 | odd | 6 | inner | ||
49.6.c.g.18.2 | 4 | 7.4 | even | 3 | inner | ||
49.6.c.g.30.1 | 4 | 7.6 | odd | 2 | inner | ||
49.6.c.g.30.2 | 4 | 1.1 | even | 1 | trivial | ||
441.6.a.u.1.1 | 2 | 21.5 | even | 6 | |||
441.6.a.u.1.2 | 2 | 21.2 | odd | 6 | |||
784.6.a.z.1.1 | 2 | 28.19 | even | 6 | |||
784.6.a.z.1.2 | 2 | 28.23 | odd | 6 |